报告题目: Deformation of 3-Lie algebras and symplectic structures

报告人：生云鹤教授 吉林大学

报告时间：2018年1月18日上午9:00-10:00

报告地点：数学与统计学院一楼北研教室

报告摘要: In the first part of the talk, Iwe study deformations of 3-Lie algebras and introduce the notion of a Nijenhuis operator on a 3-Lie algebra. In the sencond part of the talk, we use the Nijenhuis condition obtained above to give the integrability conditions of product structures and complex structures on a 3-Lie algebra. A 3-Lie algebra enjoys a product structure if and only if it is the direct sum (as vector spaces) of two subalgebras. We find that there are four types special integrability conditions, and each of them gives rise to a special decomposition of the original 3-Lie algebra. They are also related to O-operators, Rota-Baxter operators and matched pairs of 3-Lie algebras. Parallelly, we introduce the notion of a complex structure on a 3-Lie algebra and there are also four types special integrability conditions. If time permitted, we add compatibility conditions between a complex structure and a product structure, between a symplectic structure and a paracomplex structure, between a symplectic structure and a complex structure, to introduce the notions of a complex product structure, a para-K\"{a}hler structure and a pseudo-K\"{a}hler structure on a 3-Lie algebra. We use 3-pre-Lie algebras to construct these structures.

报告人简介：生云鹤，吉林大学数学与统计学院教授，博士生导师，研究兴趣：数学物理、Poisson几何、高阶李理论。